Method and apparatus for characterizing resonator elements

Abstract

This paper provides a method for characterizing a resonator element (102). The method includes providing a laser with a tunable carrier frequency and coupling at least a first portion of the laser to a resonator element (102) having a plurality of carrier resonances (3000) for the carrier frequency of the laser, wherein adjacent carrier resonances (3000) are spaced apart from each other by a free spectral region (FSR) in the spectral domain. The method further includes modulating the intensity and / or phase of the portion of the laser coupled to the resonator element (102) with a first modulation frequency (1001) and a second modulation frequency (1002), thereby generating at least two sideband resonances (3001) separated from the corresponding carrier resonance (3000) by the first modulation frequency (1001), and generating at least two sideband resonances (3002) separated from the corresponding carrier resonance (3000) by the second modulation frequency (1002), wherein the first modulation frequency (1001) and the second modulation frequency (1002) are not integer multiples of the free spectral region and are not identical to each other. Furthermore, the method includes tuning the carrier frequency of the laser at a predetermined tuning rate and measuring the intensity of the laser transmitted and / or reflected by the resonator element (102) while tuning the carrier frequency. Additionally, the method includes measuring the tuning time for tuning the carrier frequency through four adjacent sideband resonances, the tuning time being equivalent to the tuning time required to change the tunable carrier frequency from the value corresponding to the first resonance (3001, 3002) of the four sideband resonances to the value corresponding to the last resonance (3001, 3002). Furthermore, the method includes determining the interval between multiple carrier resonances (3000) in the spectral domain based on the measured intensity of the laser transmitted and / or reflected by the resonator element (102) and using a first modulation frequency (1001), a second modulation frequency (1002), and the measured tuning time for tuning the carrier frequency through four adjacent sideband resonances (3001, 3002).

Description

Technical Field

[0001] This disclosure provides a method and apparatus for characterizing resonator elements, a method and apparatus for providing an optical frequency reference, a LIDAR system, and a gas sensing system. Therefore, this disclosure relates to techniques for providing optical frequency references. Background Technology

[0002] Many applications benefit from the ability to measure the time difference and / or spectral difference between multiple signals with high precision.

[0003] In many applications, optical frequency combs can be used for this purpose, as seen in the paper "Carrier-Envelope Phase Control of Femtosecond Mode-Locked Lasers and Direct Optical Frequency Synthesis" by DJ Jones, SADiddams, JKRanka, A. Stentz, R.S. Windeler, J.L. Hall, and S.T. Cundiff, *Science*, Vol. 288, pp. 635-639 (2000), and by R. Holzwarth, Th. Udem, and T.W. J.K. Night, W.J. Wadsworth, and P. St.J. Russell, “Optical Frequency Synthesizer for Precision Spectroscopy,” Physical Review Letters, Vol. 85, pp. 2264–2267 (2000). These techniques enable single-frequency metrology with up to 18-digit accuracy; see M. Takamoto, I. Ushijima, N. Ohmae, T. Yahagi, K. Kokado, H. Shinkai, and H. Katori, “Test of general relativity by a pair of transportable opticallattice clocks,” Nature Photonics, Vol. 14, pp. 411–415 (2020).

[0004] In addition to single-frequency metrology, optical frequency combs are also used for high-precision and high-speed broadband spectral analysis, thanks to their unique combination of large bandwidth and high spectral resolution. Over the past two decades, various spectroscopic methods based on optical frequency combs have been developed, such as direct frequency comb spectroscopy, dual-comb spectroscopy, and Fourier transform spectroscopy.

[0005] Despite their high precision and wide range of applications, frequency combs often suffer from low power and spectral amplitude fluctuations in each comb line. This limits their use and poses a challenge to their further applications. See T. Fortier and E. Baumann's paper "20 years of developments in optical frequency comb technology and applications", Communications Physics, Vol. 2, pp. 1–16 (2019).

[0006] Furthermore, high-precision measurements based on optical frequency combs typically require a frequency comb light source with long-term coherence, which involves complex servo circuits, see N. Picqué and TW. The paper “Frequency combspectroscopy”, Nature Photonics, Vol. 13, pp. 146–157 (2019).

[0007] In existing technologies, micro-resonators are typically pumped using a modulated laser to generate a frequency comb, where the center frequency of the laser radiation coupled to the resonator element remains constant. The carrier frequency of the laser radiation coupled to the resonator element usually needs to be stabilized. To generate the frequency comb, laser radiation spanning octave bands is typically required, which overlap spectrally, resulting in high technical complexity and cost.

[0008] Therefore, overcoming the above limitations is essential. Summary of the Invention

[0009] The solutions to the above problems are: a method and apparatus for characterizing resonator elements, a method and apparatus for providing an optical frequency reference signal for a laser with a tunable carrier frequency, a LiDAR system, and a gas sensing system, all of which have the features of their respective independent claims. Optional embodiments are provided in the dependent claims and the specification.

[0010] In one aspect, a method for characterizing a resonator element is provided. The method includes providing a laser source having a tunable carrier frequency and coupling at least a first portion of the laser to a resonator element having multiple carrier resonances at the carrier frequency of the laser, wherein adjacent carrier resonances are spaced apart from each other by free spectral regions in the spectral domain. The method includes modulating the intensity and / or phase of a portion of the laser coupled to the resonator element at a first modulation frequency and a second modulation frequency, thereby generating at least two sideband resonances separated from the corresponding carrier resonance by the first modulation frequency for each carrier resonance, and generating at least two sideband resonances separated from the corresponding carrier resonance by the second modulation frequency, wherein the first modulation frequency and the second modulation frequency are not integer multiples of the free spectral regions and are not identical to each other. Furthermore, the method includes tuning the carrier frequency of the laser at a predetermined tuning rate, measuring the laser intensity transmitted and / or reflected by the resonator element while tuning the carrier frequency, and measuring the tuning time when the carrier frequency is tuned through four adjacent sideband resonances, the tuning time being equivalent to the tuning time required to change the tunable carrier frequency from a value corresponding to the first of the four sideband resonances to a value corresponding to the last of the four sideband resonances. The method further includes determining the interval between multiple carrier resonances in the spectral domain based on the measured intensity of the laser transmitted and / or reflected by the resonator elements and the measured tuning time of the first modulation frequency, the second modulation frequency, and the tuning carrier frequency after four adjacent sideband resonances.

[0011] In another aspect, an apparatus for characterizing a resonator element is provided. The apparatus includes a tunable laser source (for emitting laser light having a tunable carrier frequency) and a coupling element (for coupling at least a portion of the laser light into the resonator element). Furthermore, the apparatus includes a modulator for modulating the intensity and / or phase of the portion of the laser light coupled into the resonator element, thereby generating at least two sideband resonances at a first modulation frequency for each carrier resonance, spaced apart from the corresponding carrier resonance by the first modulation frequency, and at a second modulation frequency, generating at least two sideband resonances at a second modulation frequency, spaced apart from the corresponding carrier resonance by the second modulation frequency. Additionally, the apparatus includes a detector unit for measuring the intensity of the portion of the laser light transmitted and / or reflected by the resonator element. The device also includes a control unit configured to tune the carrier frequency of the laser, and to determine the tuning time and the interval between multiple carrier resonances in the spectral domain based on the measured intensity of the laser transmitted and / or reflected by the resonator elements and based on the first modulation frequency, the second modulation frequency, and the measured tuning time of the tuned carrier frequency after four adjacent sideband resonances, the tuning time being equivalent to the tuning time required to change the tunable carrier frequency from the value corresponding to the first of the four sideband resonances to the value corresponding to the last of the four sideband resonances.

[0012] In another aspect, a method is provided for providing an optical frequency reference signal for a laser having a tunable carrier frequency. The method includes providing a resonator element having multiple carrier resonances for the carrier frequency of the laser, wherein adjacent carrier resonances are spaced apart from each other in the spectral domain by their respective predetermined free spectral regions. The method further includes coupling a first portion of the laser to the resonator element and tuning the carrier frequency of the laser at a predetermined tuning rate. Furthermore, the method includes using a portion of the laser transmitted and / or reflected by the resonator element as an optical frequency reference signal for spectral scanning, wherein the intensity of the laser transmitted and / or reflected by the resonator element has local extrema in frequency, these frequencies being spaced apart from each other in the spectral domain by FSR.

[0013] On the other hand, the optical frequency reference signal provided by the method according to this disclosure can be used as a spectral reference marker.

[0014] On the other hand, a method for spectrally characterizing an analyte is provided, the method comprising providing an optical frequency reference signal according to a disclosed method, and using the optical frequency reference signal as a spectral reference marker for spectrally characterizing the analyte. Using the optical frequency reference signal as a spectral reference marker may include determining relative spectral distances of multiple spectral features of the analyte based on one or more FSRs.

[0015] In another embodiment, an apparatus is provided for providing a laser with a tunable carrier frequency as an optical frequency reference signal. The apparatus optionally includes a tunable laser source for emitting laser light with a tunable carrier frequency. The apparatus also includes a resonator element having multiple carrier resonances for the tunable carrier frequency of the laser, wherein the carrier resonances are spaced apart from each other in the spectral domain by respective predetermined free spectral regions, and the apparatus is adapted to couple a portion of the laser light into the resonator element. The apparatus further includes a control unit that tunes the carrier frequency of the laser light at a predetermined tuning rate. The apparatus is used to use a portion of the laser light transmitted and / or reflected by the resonator element as an optical frequency reference signal for spectral scanning, wherein the intensity of the laser light transmitted and / or reflected by the resonator element has local extrema in frequency, these frequencies being spaced apart from each other in the spectrum by FSR. Optionally, the apparatus also includes a detector unit for measuring the intensity of the portion of the laser light transmitted and / or reflected by the resonator element. In addition, the device may optionally include a control unit configured to provide a frequency of a tunable carrier frequency that has a local extremum in the measured intensity of a portion of the laser transmitted and / or reflected by the resonator element, and that the frequency serves as a spectral reference marker for an optical frequency reference signal defined by a predetermined free spectral region.

[0016] In another aspect, a LIDAR system is provided. The LIDAR system includes means for providing an optical frequency reference signal according to the present disclosure.

[0017] In another aspect, a gas sensing system is provided, which includes means according to the present disclosure for providing an optical frequency reference signal.

[0018] In another aspect, a method for characterizing a resonator element is provided. The method includes providing a laser source having a tunable carrier frequency and coupling at least a first portion of the laser to a resonator element having multiple carrier resonances at the carrier frequency of the laser, wherein adjacent carrier resonances are spaced apart from each other by free spectral regions in the spectral domain. The method further includes modulating the intensity and / or phase of a portion of the laser coupled to the resonator element with a first modulation frequency to generate at least two sideband resonances separated from the corresponding carrier resonance by the first modulation frequency, wherein the first modulation frequency is not an integer multiple of the free spectral regions. Furthermore, the method includes tuning the carrier frequency of the laser at a predetermined tuning rate and measuring the intensity of laser transmitted and / or reflected by the resonator element while tuning the carrier frequency. The method also includes measuring the tuning time between the multiple carrier resonances that are spaced apart from each other by at least twice the first modulation frequency. Additionally, the method includes determining the interval between multiple free spectral regions in the spectral domain based on the measured intensity of the laser transmitted and / or reflected by the resonator element, using the first modulation frequency and the measured tuning time between the multiple carrier resonances that are spaced apart from each other by at least twice the first modulation frequency.

[0019] A laser with a tunable carrier frequency is a coherent light, the center frequency of which can be tuned by the light source. Tuning the carrier frequency can be considered as changing the carrier frequency over time, optionally in a continuous manner. Tuning the carrier frequency may include, for example, sweeping the carrier frequency in a sinusoidal manner.

[0020] A resonator element is an element with specific transmission and / or absorption characteristics for a tunable carrier frequency, wherein, for a predetermined value of the tunable carrier frequency, the resonator element exhibits local minima and / or maxima of transmission and / or absorption and / or reflection. In particular, the resonator element may include a resonant cavity that satisfies a resonance condition for a specific value of the tunable carrier frequency. These specific carrier frequency values ​​are considered carrier resonances. In the case of a resonant cavity, transmission may exhibit local minima at these frequencies, where the tunable carrier frequency resonates according to the length of the resonant cavity. Measuring the laser intensity transmitted and / or reflected by the resonator element while tuning the carrier frequency refers to measuring the laser intensity and / or power transmitted through and / or reflected by the resonator element while continuously tuning the carrier frequency.

[0021] Modulating the intensity and / or phase of a portion of the laser using a first modulation frequency and an optional second modulation frequency means that the intensity and / or phase of the laser changes periodically with the first modulation frequency and the optional second modulation frequency. Therefore, modulating the laser intensity with the first modulation frequency and the second modulation frequency results in the intensity periodically decreasing and increasing with the time variation of the modulation signals at the first and second modulation frequencies. If there is more than one modulation signal and more than one modulation frequency, then the modulation may actually be a superposition of the individual modulation signals. This can be achieved by applying the first and second modulation frequencies using a power combiner. The first and second modulation frequencies may be higher than the free spectral range of the laser and the resonator elements. While a first modulation signal and a second modulation signal with a first modulation frequency and a second modulation frequency are explicitly mentioned, it should be noted that, according to some alternative embodiments, the laser may be modulated by more than two modulation signals at more than two modulation frequencies. The first and second modulation frequencies may both be within the radio frequency range. In particular, the first and second modulation frequencies are each in the range of approximately 100 MHz to approximately 100 GHz. The free spectral range of the resonator elements may be selected to be not less than 1 MHz and not greater than 100 GHz.

[0022] The modulation index of the modulation depth for intensity modulation and / or phase modulation ranges from approximately 0.6 to 2.

[0023] Sideband resonances originating from laser intensity and / or phase modulation may arise from the superposition of the carrier frequency and one or more modulation frequencies.

[0024] The modulation frequency is not an integer multiple of the free spectral region and they are not the same. This means that the sideband resonances generated by the modulation frequency do not completely overlap with the carrier resonance, nor do they completely overlap with other sideband resonances originating from other modulation frequencies.

[0025] The tuning time for the carrier frequency through four adjacent sideband resonances is equivalent to the tuning time required to change the tunable carrier frequency from the value corresponding to the first of the four sideband resonances to the value corresponding to the last of the four sideband resonances. However, according to other embodiments, the carrier frequency adjustment can be performed in a non-uniform but determinate manner. Furthermore, if the time interval between the four adjacent sideband resonances is sufficiently small, a detailed understanding of the tuning characteristics may not be necessary. Based on the measured tuning time, the spectral difference between the first and last sideband resonances can be determined.

[0026] Tunable laser sources may include tunable continuous wave laser sources. Tunable laser sources may include or may consist of diode lasers.

[0027] The modulator may include or consist of an acousto-optic modulator and / or an electro-optic modulator, and may also be implemented by modulating laser current and / or laser current. The detector unit may include one or more photodiodes, which are sensitive to the tuning range of a laser having a tunable carrier frequency. In particular, the modulator can be used to modulate the intensity and / or phase of the transmitted laser.

[0028] The control unit can be an electrical and / or electronic device, such as a computer, smartphone, integrated circuit, and / or tablet. The control unit can be connected to the detector unit to receive data measured by the detector unit. The control unit can also be connected to a tunable light source and configured to send commands to the tunable light source to tune the carrier frequency in a specific manner.

[0029] A tunable carrier frequency having local extrema in the measured intensity of the laser portion transmitted and / or reflected by the resonator elements is provided as a spectral reference mark for an optical frequency reference signal defined by a predetermined free spectral region (FSR). This means that a specific frequency that will appear as a local extrema is defined as the spectral reference mark. In other words, the resonator elements are used in such a way that their predetermined, well-characterized carrier resonances are used as optical frequency reference values, because their spectral distances can be well determined and characterized according to the characterization process of this disclosure. The well-characterized spectral distances between carrier resonances corresponding to the free spectral region and / or the spectral distances between sideband resonances can be provided as optical reference frequencies, and therefore also as optical frequency reference signals.

[0030] The advantage of this disclosure lies in its ability to provide a high-precision optical frequency reference signal. In particular, compared to conventional techniques for providing frequency reference signals (such as frequency combs), this invention can provide a high-precision frequency reference signal at a lower technical cost. According to the disclosed information, the frequency reference signal can be provided based on standard optical and electronic components, which are less expensive than conventional frequency combs. It is important to emphasize that, according to the disclosure, the optical frequency reference signal can be provided based on a continuous-wave laser (such as a diode laser) without the need for octave-band transspectral and nonlinear optical processes (which are typically required in frequency combs). Therefore, this invention can provide an optical frequency reference signal with lower technical complexity, without the need for expensive components, thus enabling the provision of an optical frequency reference signal at a lower cost. Furthermore, the lower technical complexity of these devices allows for the provision of smaller and / or more compact devices, which can be miniaturized and / or integrated into other compact optical and / or electronic components. In particular, according to the disclosed information, a continuous-wave laser can be used, wherein the carrier frequency, i.e., the center frequency of the laser radiation, can be swept within a predetermined spectral region, for example, optionally 10 free spectral regions. During tuning, the carrier frequency and tuning rate are likely known, allowing for a predetermined frequency sweep of the carrier frequency within the tuning time. Therefore, this disclosure allows for the characterization of resonator elements and / or the provision of a frequency reference signal without the need for a frequency comb or other hardware that is significantly more expensive and complex. Thus, according to the technical solution of this disclosure, it is unnecessary to generate a frequency comb within the resonator element. For spectral applications, the carrier frequency can be tuned within a predetermined tuning range, including tuning within the spectral range required for the spectral application.

[0031] Therefore, compared to conventional frequency combs, the advantages of this disclosure lie in providing optical frequency reference signals with lower technical complexity, smaller size, and lower cost. According to the method and apparatus of this disclosure, there is no need for octave-span and spectrally stable laser radiation to overlap spectrally; instead, only a laser with a tunable carrier frequency needs to be provided, and the carrier frequency needs to be tuned at a predetermined tuning rate within a predetermined spectral region (e.g., 10 free spectral regions). Therefore, compared to the prior art, the technical complexity and requirements can be significantly reduced.

[0032] The difference between the first and second modulation frequencies can be chosen to be no less than 10% of the resonant linewidth of the carrier resonance and no more than 50% of the free spectral region. This ensures appropriate differentiation between sideband resonances and between sideband resonances and the carrier resonance, as their spacing in the frequency domain is sufficiently large. The first and second modulation frequencies essentially correspond to frequencies near multiples of n+1 / 2 of the free spectral region, where n is an integer. "Near" means that the frequency is close to, but not exactly the same as, a multiple of the free spectral region. For example, the first and / or second modulation frequencies can maintain a certain spectral spacing with multiples of n+1 / 2 of the free spectral region between 100 MHz and 100 GHz, respectively. This ensures that the sideband resonances are located appropriately between the carrier resonances in the spectrum.

[0033] Two sideband resonances generated by a first modulation frequency from one of the carrier resonances can be located within at least one free spectral region, as can at least two sideband resonances generated by a second modulation frequency from one of the carrier resonances. This allows for the precise determination of the spectral interval between two adjacent carrier resonances using the spectral intervals between the first and second modulation frequencies and between them and the relevant carrier frequencies, thereby determining the spectral interval of the free spectral region.

[0034] Measuring the tuning time of a carrier frequency through four adjacent sideband resonances can include measuring the tuning time of the carrier frequency through four adjacent sideband resonances within a single free spectral region. The advantage of this is that the spectral tuning range required to determine the intervals between multiple carrier resonances can be limited to a smaller spectral range. This helps maintain a constant tuning rate of the laser source within the smaller spectral range that needs to be covered, thereby reducing or avoiding unnecessary measurement errors when determining the intervals between carrier resonances.

[0035] The method for characterizing resonator elements may further include the steps of: coupling a second portion of a laser to a calibration element having predetermined absolute transmission and / or reflection characteristics, and measuring the intensity of the laser portion transmitted and / or reflected by the calibration element while tuning the carrier frequency. Furthermore, the method includes the steps of: identifying at least one specific absolute transmission and / or reflection characteristic of the calibration element having a predetermined frequency that coincides with or has a specified offset from one of the carrier resonances or sideband resonances in the frequency domain, and controlling a control unit adapted to calibrate the absolute frequency of at least one of the carrier resonances or sideband resonances according to the identified specific absolute transmission and / or reflection characteristics of the calibration element. Therefore, these additional steps based on the calibration element enable absolute calibration of the spectral frequencies of the carrier resonances and sideband resonances. While the aforementioned steps allow for relative calibration of the carrier resonances and sideband resonances, these additional steps allow for absolute calibration of at least one of the carrier resonances and sideband resonances, and, through a single absolutely calibrated carrier resonance or sideband resonance, calibration of all remaining carrier resonances and sideband resonances by relative calibration according to the modulation frequency. Therefore, this method can perform absolute calibration of the resonator element, which is then used to provide an absolute optical frequency reference signal. Thus, the apparatus for characterizing the resonator element can further include a calibration element having predetermined absolute transmission and / or reflection characteristics, wherein the detector unit is further adapted to measure the intensity of a portion of the laser transmitted and / or reflected by the calibration element while tuning the carrier frequency. The control unit is also adapted to identify at least one specific absolute transmission and / or reflection characteristic of the calibration element having a predetermined frequency that coincides with or has a specified offset from one of the carrier resonances or sideband resonances in the frequency domain, and the control unit is adapted to calibrate the absolute frequency of at least one of the carrier resonances or sideband resonances based on the identified specific absolute transmission and / or reflection characteristics of the calibration element.

[0036] The calibration element may include a gas chamber filled with a predetermined gas, which has at least one specific absolute transmission and / or reflection characteristic. The advantage of using a gas chamber is that the absorption characteristics of many gases are precisely characterized and well understood from the literature, such as distinct absorption lines. Therefore, the absorption and transmission characteristics can be well used as absolute calibration references when comparing the carrier resonances and / or sideband resonances of resonator elements. Alternatively or additionally, the calibration element may also include one or more of the following elements: a frequency comb, a wavelength meter, or elements providing atomic and / or molecular transition lines.

[0037] Resonator elements may include fiber optic cavities and / or integrated waveguide resonators, and / or whispering-gallery mode resonators, and / or Etalon resonators and / or Fabry-Perot resonators. This allows resonator elements to be integrated into conventional optical and / or electronic devices and apparatuses. Furthermore, such resonator elements enable device miniaturization, allowing for integration into small-scale optical and / or electronic devices.

[0038] This method provides an optical frequency reference signal for a laser with a tunable carrier frequency. It includes modulating the intensity and / or phase of a portion of the laser coupled to a resonator element at a first modulation frequency and a second modulation frequency, thereby generating at least two sideband resonances separated from the corresponding carrier resonance by the first modulation frequency, and at least two sideband resonances separated from the corresponding carrier resonance by the second modulation frequency, wherein the first and second modulation frequencies are not integer multiples of the free spectral region and are mutually exclusive. The method provides the sideband resonance frequencies as spectral reference markers for the optical frequency reference signal. If the provided resonator element is already calibrated and recalibration is not required, the calibration process can be omitted. However, in some embodiments, the method for providing an optical frequency reference signal for a laser with a tunable carrier frequency may also include a process of calibrating and / or recharacterizing the resonator element. This allows for periodic checks of the resonator element's calibration, thereby ensuring and potentially improving the accuracy of the provided optical frequency reference signal. Related methods for characterizing the resonator element correspond to those further described above. Furthermore, in this case, the first modulation frequency and the second modulation frequency can each be located within a radio frequency range, specifically within a range of approximately 100 MHz to approximately 10 GHz. The difference between the first modulation frequency and the second modulation frequency can be selected to be no less than 10% of the resonant linewidth of the carrier resonance and no more than 50% of the free spectral region. The first modulation frequency and the second modulation frequency substantially correspond to frequencies near multiples of n+1 / 2 in the free spectral region, where n is an integer.

[0039] Furthermore, the method may further include absolute calibration of the provided optical frequency reference signal. The method may include coupling a second portion of a laser to a calibration element having predetermined absolute transmission and / or reflection characteristics, and measuring the intensity of the laser portion transmitted and / or reflected by the calibration element while tuning the carrier frequency. The method also includes identifying at least one specific absolute transmission and / or reflection characteristic of the calibration element having a predetermined frequency that coincides with or has a specified offset from one of the carrier resonances or sideband resonances in the frequency domain, and a control unit adapted to calibrate the absolute frequencies of the carrier resonances and / or sideband resonances according to the identified specific absolute transmission and / or reflection characteristics. In this way, the method can periodically perform absolute recalibration of the resonator elements, thereby calibrating the provided optical frequency reference signal. The calibration element includes a gas chamber filled with a predetermined gas having at least one specific absolute transmission and / or reflection characteristic, and / or includes a frequency comb and / or a wavelength meter and / or a system providing atomic transition lines.

[0040] The carrier frequency of the laser is tuned within at least ten free spectral regions. The tuning of the carrier frequency is performed according to predetermined tuning modes. These predetermined tuning modes include sweeping the carrier frequency in sinusoidal tuning and / or sawtooth tuning modes. This provides an optical frequency reference signal in a fast, reliable, and / or low-tech and low-cost manner.

[0041] The laser can be a continuous-wave laser. The spectral width of the laser may be smaller than the linewidth of the resonator element. During a tuning time of approximately 5 μs and / or a measurement time, the typical short-term linewidth of the laser light may be 100 kHz or less. This allows for high-precision measurements.

[0042] Therefore, the apparatus for providing an optical frequency reference signal for a laser with a tunable carrier frequency can be used to characterize resonator elements and / or perform relative and / or absolute calibration of the resonator elements and carrier resonances and / or sideband resonances. Thus, the apparatus for providing an optical frequency reference signal for a laser with a tunable carrier frequency may further include a modulator for modulating the intensity and / or phase of a portion of the laser coupled to the resonator elements at a first modulation frequency, thereby generating at least two sideband resonances separated from the corresponding carrier resonance by the first modulation frequency for each carrier resonance. The control unit may also be configured to provide a frequency of the tunable carrier frequency, which has local extrema due to sideband resonances in the measured intensity of the portion of the laser transmitted and / or reflected by the resonator elements, as a spectral reference marker for an optical frequency reference signal defined by a predetermined free spectral region and the first modulation frequency. The resonator elements may include fiber optic cavities and / or integrated waveguides, and / or whispering-gallery mode resonators and / or Etalon resonators and / or Fabry-Perot resonators. The modulator may include electro-optic intensity and / or phase modulators.

[0043] Furthermore, the apparatus for providing an optical frequency reference signal for a laser with a tunable carrier frequency may further include a calibration element having predetermined absolute transmission and / or reflection characteristics. The detector unit can also measure the intensity of a portion of the laser transmitted and / or reflected by the calibration element while tuning the carrier frequency. The control unit is also adapted to identify at least one specific absolute transmission and / or reflection characteristic of the calibration element having a predetermined frequency that coincides with or has a specified offset from one of the carrier resonances or sideband resonances in the frequency domain, and the control unit is adapted to calibrate the absolute frequency of at least one of the carrier resonances or sideband resonances based on the identified specific absolute transmission and / or reflection characteristics of the calibration element. This allows for absolute (re)calibration of the resonator element and the optical frequency reference signal. The calibration element may include a gas chamber filled with a predetermined gas having at least one specific absolute transmission and / or reflection characteristic, and / or include a frequency comb and / or a wavelength meter and / or elements or systems providing atomic and / or molecular transition lines.

[0044] Tunable laser sources may include tunable continuous wave laser sources. Tunable laser sources may include diode lasers. Tunable laser sources are used to emit tunable lasers with a spectral width smaller than the linewidth of the resonator element.

[0045] The LIDAR system includes means for providing an optical frequency reference signal according to this disclosure, which can be used to reference a tunable laser to the optical reference signal provided by the means. In some conventional systems known in the prior art, the tunable laser is referenced to a frequency comb for the purpose of achieving high precision, high accuracy, and high measurement speed. In this case, the frequency comb provides an optical frequency reference signal. Such devices are referenced in the following papers: “Comb-calibrated frequency-modulated continuous-waveladar for absolute distance measurements”, Optics Letters, Vol. 38, No. 12, pp. 2026-2028, 2013; “Comb-calibrated laserranging for three-dimensional surface profiling with micrometer-level precision at a distance”, Optics Express, Vol. 22, No. 21 (2014), pp. 24914-24928; and “Comb-calibrated frequency sweeping interferometry for absolute distance and vibration measurement”, Optics Letters, Vol. 44, No. 20 (2019), pp. 5069-5072.

[0046] However, frequency combs typically suffer from drawbacks such as technical complexity, sensitivity to environmental influences, and high cost. The disclosed LIDAR system provides calibrated resonator elements, such as fiber optic cavities characterized and / or calibrated according to the methods disclosed herein, to provide an optical frequency reference signal. Compared to frequency combs, the disclosed LIDAR system achieves high precision, high accuracy, and high measurement speed, while also being less costly and less technically complex. Therefore, using the apparatus of this disclosure to provide an optical frequency reference signal can achieve high precision comparable to that of a frequency comb with significantly reduced technical complexity and cost. Thus, LIDAR and many other applications can achieve high precision, low complexity, and high stability at a lower cost using this invention, advantages that are economically impossible to achieve with a frequency comb. It is important to emphasize that the LIDAR apparatus includes means for providing a frequency reference signal according to this disclosure; therefore, only calibrated resonator elements are required, without the need for a modulator. However, according to some embodiments, an intensity modulator may also be provided, for example, for recalibrating the resonator elements.

[0047] Similarly, the gas sensing system disclosed herein includes a means for providing an optical frequency reference signal, which can be adjusted in a manner similar to conventional greenhouse gas frequency remote sensing systems, see Nishiyama, Akiko, Daiki Ishikawa and Masatoshi Misono, “High resolution molecular spectroscopic system assisted by an optical frequency comb,” JOSA B, Vol. 30, No. 8 (2013), pp. 2107-2112; Rieker, Gregory B et al., “Frequency-comb-based remote sensing of greenhouse gases over kilometer air paths,” Optica, Vol. 1, No. 5 (2014), pp. 290-298; Herman Daniel I et al., “Precise multispecies agricultural gas flux determined using broadband open-path dual-comb spectroscopy,” Science Advances, Vol. 7, No. 14 (2021), eabe9765.

[0048] In this case, a resonator-based device can be used instead of a frequency comb. The resonator element is calibrated according to the method disclosed herein, and can achieve the same high precision, accuracy and measurement speed as the frequency comb-based device, but with much lower technical complexity, much lower manufacturing cost and higher robustness.

[0049] Those skilled in the art will understand that the features described above, as well as those in the following description and figures, are disclosed not only in the explicitly disclosed embodiments and combinations, but also include other technically feasible combinations and independent features. Several alternative embodiments and specific examples will be described below with reference to illustrations to illustrate the contents of this disclosure, but the disclosure is not intended to be limited to the described embodiments. Attached Figure Description

[0050] The following description, with reference to the accompanying drawings, further illustrates optional embodiments and examples.

[0051] Figure 1 An apparatus for characterizing resonator elements is shown according to an optional embodiment.

[0052] Figure 2 Describes the use Figure 1 The method for characterizing resonator elements using a device.

[0053] Figure 3 It demonstrates carrier resonance and sideband resonance.

[0054] Figure 4 An apparatus for characterizing resonator elements, designed according to an alternative embodiment, is shown.

[0055] Figure 5 An apparatus is described that provides an optical frequency reference signal for a laser having a tunable carrier frequency.

[0056] Figure 6 A method for providing an optical frequency reference signal for a laser with a tunable carrier frequency is illustrated.

[0057] Figure 7 and Figure 8 The results of a method for characterizing a resonator element according to an alternative embodiment are shown.

[0058] Figure 9 The results of the method for providing an optical frequency reference signal are shown.

[0059] Figure 10 The results of absolute calibration using calibration elements are shown.

[0060] Figure 11 A LiDAR designed according to an optional embodiment is illustrated.

[0061] Figure 12 A gas sensing system designed according to an alternative embodiment is illustrated schematically.

[0062] In different accompanying drawings, the same reference numerals are used for corresponding or similar features. Detailed Implementation

[0063] Figure 1 An apparatus 100 for characterizing a resonator element 102, according to an alternative embodiment, is shown. The resonator element 102, which is composed of a fiber optic cavity resonator, represents the device under test and is characterized by the apparatus 100.

[0064] The apparatus 100 includes a tunable laser source 104 for emitting laser light with a tunable carrier frequency. According to the illustrated embodiment, the output of the laser source 104 is directly coupled to an optical fiber, which in turn is coupled to a resonator element 102. Therefore, the optical fiber 106 can act as a coupling element 108, coupling at least a portion of the laser light to the resonator element 102.

[0065] Furthermore, the device 100 includes a modulator 110 (which may be an opto-modulator) for modulating the intensity and / or phase of a portion of the laser coupled to the resonator element 102. Modulation is performed at a first modulation frequency 1001 and a second modulation frequency 1002. Modulation at the first modulation frequency 1001 generates at least two sideband resonances for each carrier resonance, and these at least two sideband resonances are separated from their corresponding carrier resonances by the first modulation frequency 1001. Modulation at the second modulation frequency 1002 generates at least two sideband resonances for each carrier resonance, and these at least two sideband resonances are separated from their corresponding carrier resonances by the second modulation frequency 1002. The modulator may be an electro-optic modulator for modulating the intensity or phase of the laser. One, two, or more modulation signals, such as the first modulation frequency 1001 and the second modulation frequency 1002, may be applied to the modulator. However, it should be emphasized that, according to certain alternative embodiments, only one modulation frequency may be used. The modulation signal applied to the modulator 110 may be a superposition of the first modulation frequency 1001 and the second modulation frequency 1002. The first modulation frequency 1001 and the second modulation frequency 1002 may represent sinusoidal oscillations at their respective modulation frequencies. However, according to some alternative embodiments, the modulation signal may be a more complex modulation signal, such as a waveform covering a wider range in the spectral domain, and / or a continuous oscillation deviating from a sinusoidal oscillation, such as a sawtooth signal. Furthermore, a bias voltage 1004 may be applied to the modulator 110, for example, to set the basic transmission characteristics of the modulator 110.

[0066] The laser beam enters the device under test (i.e., resonator element 102) after passing through modulator 110.

[0067] Downstream of resonator element 102, device 100 includes detector unit 112 for measuring the intensity of a portion of the laser transmitted and / or reflected by resonator element 102. According to the illustrated embodiment, detector unit 112 is used to detect the intensity of the laser transmitted through resonator element 102. Detector unit 112 may include one or more photodiodes sensitive to the carrier frequency of the laser. Detector unit 112 may further include or be connected to data logger unit 114 for storing and / or visualizing and / or evaluating the output signal provided by photodiode 112.

[0068] Furthermore, the device 100 includes a control unit 116 configured to tune the carrier frequency of the laser, and to determine the tuning time and the interval between multiple carrier resonances in the spectral domain based on the measured intensity of the laser transmitted and / or reflected by the resonator element 102, and based on the first modulation frequency 1001, the second modulation frequency 1002, and the measured tuning time for tuning the carrier frequency through four adjacent sideband resonances. The control unit 116 is communicatively connected to the detector unit 112 and / or a data logger for retrieving data measured by the detector unit 112. The control unit 116 is also connected to the laser source 104 for controlling the laser source 104 to adjust the carrier frequency of the laser emitted by the laser source 104. Additionally, the control unit 116 is connected to the modulator 110 and can be used to provide the modulator 110 with modulation signals, such as the first modulation frequency 1001 and the second modulation frequency 1002.

[0069] By scanning the carrier frequency (i.e., the center wavelength of the laser) emitted by the laser source 104, the laser coupled to the resonator element 102 will generate multiple carrier resonances in the resonator element 102 during the tuning process. For the frequency value corresponding to the carrier resonance, a large amount of laser energy is stored in the resonator element 102. Therefore, at the frequency corresponding to the carrier resonance, the transmission intensity through the resonator element 102 will decrease. Thus, the carrier resonance can be identified by the local minimum of the transmitted energy detected by the detector unit 102. Furthermore, since the intensity and / or phase of the laser coupled to the resonator element 102 is modulated using the first modulation frequency 1001 and the second modulation frequency 1002, two frequency sidebands are generated. For each modulation frequency, the two frequency sidebands will generate corresponding two sideband resonances at a specific frequency different from the carrier resonance, and the two frequency sidebands are spaced apart from the carrier frequency by the first modulation frequency 1001 and the second modulation frequency 1002 in the frequency domain, respectively, as will be referred to below. Figure 3 Further detailed description.

[0070] Based on the tuning time and the spacing between multiple carrier resonances in the spectral domain, the measured intensity of the laser transmitted and / or reflected by the resonator element 102, and based on the first modulation frequency 1001, the second modulation frequency 1002, and the measured tuning time for tuning the carrier frequency through four adjacent sideband resonances, the control unit 116 can determine the spectral spacing between carrier resonances, thereby determining the spectral range of the resonator element 102. Therefore, this device can accurately describe the spectral characteristics of the resonator element 102.

[0071] The following will refer to Figure 2 Explanation of usage Figure 1 The aforementioned device is a method for characterizing resonator elements.

[0072] The method includes a first step 202, which provides a laser with a tunable carrier frequency.

[0073] Another step 204 includes coupling at least a first portion of the laser to a resonator element 102, the resonator element 102 having multiple carrier resonances for the carrier frequency of the laser, wherein adjacent carrier resonances are spaced apart from each other in the spectral domain by free spectral regions.

[0074] Step 206 includes modulating the intensity and / or phase of a portion of the laser coupled to the resonator element 102 with a first modulation frequency 1001 and a second modulation frequency 1002, thereby generating at least two sideband resonances separated from the corresponding carrier resonance by the first modulation frequency for each carrier resonance, and generating at least two sideband resonances separated from the corresponding carrier resonance by the second modulation frequency. The first modulation frequency 1001 and the second modulation frequency 1002 are not integer multiples of the free spectral region and are not identical to each other.

[0075] Step 208 includes tuning the carrier frequency of the laser at a predetermined tuning rate.

[0076] Step 210 includes measuring the intensity of laser transmitted and / or reflected by the resonator element 102 while tuning the carrier frequency.

[0077] Step 212 includes measuring the tuning time of the carrier frequency through four adjacent sideband resonances.

[0078] Step 214 includes determining the interval between multiple carrier resonances in the spectral domain based on the measured intensity of the laser transmitted and / or reflected by the resonator element 102 and based on the first modulation frequency 1001, the second modulation frequency 1002, and the measured tuning time for tuning the carrier frequency through four adjacent sideband resonances.

[0079] Because the intensity and / or phase of the laser are modulated using the first modulation frequency 1001 and the second modulation frequency, when the carrier frequency is tuned, i.e., the frequency of the scanning laser source is tuned, four sideband resonances will be generated in a free spectral region (FSR) between two adjacent carrier resonances in the detection signal, such as... Figure 3 As shown. Based on the FSR of resonator element 102, Figure 3 The middle is represented as f mod1 and f mod2 The two modulation frequencies 1001 and 1002 can be set to approximately (n+1 / 2)×FSR, limited by the spectral bandwidth of the modulator, where n is an integer. The frequency difference f between the first and second modulation frequencies 1001 and 1002 is determined based on the structural linewidth of the resonator element 102. d It can be set to around a few megahertz.

[0080] exist Figure 3 In the diagram, resonance 3000 represents carrier resonance, while resonances 3001 and 3002 represent the resonance caused by the first modulation frequency 1001f. mod1 Second modulation frequency 1002f mod1 The resulting sideband resonances. Due to the potentially nonlinear behavior of the frequency scanning of the laser source 104, the time intervals t1(t3) and t2(t4) between the carrier resonance and the modulation sideband resonance within an FSR are not necessarily equal. However, the frequency interval between these two sideband resonances is constant, determined by the frequency f. mod1 or f mod2 The first or second modulation frequency 1001, 1002 is determined. Assume the FSR of the resonator element is 2×f mod1 If the modulation frequency range (which may correspond to tens of gigahertz) remains constant, then the FSR can be determined based on the first modulation frequency 1001f. mod1 Based on (2n+1)×FSR=2f mod1 +f ？ To perform calibration, where f ？ It comes from the same modulation frequency f mod1 The frequency interval between two adjacent sideband resonators 3001, such as Figure 3 As shown.

[0081] Thus, the frequency interval f ？ This becomes the only uncertainty variable in nonlinear tunable laser scanning. However, to calculate the FSR, it is necessary to calculate f. ？ For using only a single modulation frequency f mod1 The method, frequency interval f ？ The calculation can be based on the average scanning speed of the laser source 104, taking into account both the tuning time (t1+t2) and the modulation frequency (2f). mod1This allows us to determine the FSR, although to some extent f ？ Frequency uncertainty still exists.

[0082] In contrast, for using the first modulation frequency 1001f mod1 Second modulation frequency 1002f mod2 The dual RF modulation scheme has a frequency interval f. ？ It can be done on a shorter time scale T1+T2+T3 (e.g. Figure 3 The range of frequencies (shown on the right) within a small frequency range of only a few megahertz is defined. Within a single FSR, the fixed frequency interval f between the two sideband resonances is... d The first modulation frequency is 1001f mod1 Second frequency f mod2 The predetermined frequency difference between them is determined. Figure 3 The corresponding time intervals are marked with T1 3003 and T2 3004. Therefore, the frequency interval f ？ The calculation formula is T3×2f d / (T1+T2). The time interval T3 is denoted by reference numeral 3005. Thanks to the flexibility of the first and second modulation frequencies 1001 and 1002, the fixed frequency interval f between the two sideband resonances of different modulation frequencies 1001 and 1002 is achieved. d The time interval T3 can be set to a value that is very small relative to the FSR and the cavity round-trip time of the resonator element 102. Therefore, the frequency interval f ？ The uncertainty can be effectively reduced. Furthermore, by using a low FSR resonator element calibrated by dual RF modulation using a first modulation frequency 1001 and a second modulation frequency 1002, the application of the method of this application can be extended to characterizing quasi-periodic or non-quasi-periodic devices with FSR greater than the first and second modulation frequencies. Therefore, this method can characterize the resonator element 102 by determining the spectral spacing of the carrier resonance, thereby accurately determining the free spectral region. This allows the resonator element to provide an optical frequency reference signal for a laser with a tunable carrier frequency. It should be emphasized that, according to the method shown, it is only necessary to measure the tuning time of the carrier frequency tuning through four adjacent sideband resonances, the time interval of the four adjacent sideband resonances being T1+T2+T3, as shown by reference numerals 3003, 3004, and 3005 in the figures.

[0083] Figure 4 An apparatus 100 designed according to an alternative embodiment is shown. The apparatus 100 is used to characterize the properties of a resonator element 102, and is based on a reference. Figure 1 The described device 100. According to Figure 4 The optional embodiment shown describes the device with Figure 1The difference in the device lies in the addition of a calibration element 118. The calibration element 118 has predetermined absolute transmission and / or reflection characteristics, such as a predetermined absorption spectrum composed of precisely predetermined absorption lines. Furthermore, the detector unit can measure the intensity of a portion of the laser transmitted and / or reflected by the calibration element 118 while tuning the carrier frequency. For this purpose, the detector unit may include a second photodiode 112 for measuring the intensity of the laser transmitted through the calibration element 118, wherein the measurement signal of the second photodiode 112 is provided to a data logger 114 and calculated by a control unit 116. The control unit 116 is also adapted to identify at least one specific absolute transmission and / or reflection characteristic of the calibration element 118 having a predetermined frequency that coincides with or has a specified offset from one of the carrier resonances or sideband resonances in the frequency domain, and the control unit 116 is adapted to calibrate the absolute frequency of at least one of the carrier resonance 3000 or sideband resonances 3001, 3002 based on the identified specific absolute transmission and / or reflection characteristic of the calibration element 118. According to the described embodiment, the calibration element 118 includes a gas chamber containing a gas with precisely predetermined transmission and / or reflection characteristics, such as precisely defined absorption lines. This allows for absolute calibration of the spectral characteristics of the resonator element 116, since the carrier resonance 3000, sideband resonances 3001, 3002, and free spectral regions can be absolutely determined with reference to the transmission and / or reflection characteristics of the calibration element. Therefore, the resonator element 102 can be accurately characterized to provide an absolute optical frequency reference signal.

[0084] Figure 5 An apparatus 200 for providing an optical frequency reference signal for a laser with a tunable carrier frequency is described. Similar to the apparatus 100 discussed with reference to the preceding figures, apparatus 200 includes a tunable laser source 104 for emitting laser light with a tunable carrier frequency. Furthermore, apparatus 200 includes a well-characterized resonator element 102 having multiple carrier resonances for the tunable carrier frequency of the laser, wherein the carrier resonances are spaced apart from each other in the spectral domain by their respective predetermined free spectral regions (FSRs), and the apparatus is adapted to couple a portion of the laser light into the resonator element 102. Additionally, apparatus 200 includes a detector unit 112 for measuring the intensity of the laser portion transmitted and / or reflected by the resonator element 102, and a control unit 116 for providing the frequency of the tunable carrier frequency, which has local extrema in the intensity measurements of the laser portion transmitted and / or reflected by the resonator element 102, and serves as a spectral reference marker for the optical frequency reference signal defined by the predetermined free spectral regions. Figure 4 As shown, the device also includes a calibration element 118. (The last sentence appears to be incomplete and possibly contains errors. Figure 1 and Figure 4Unlike the apparatus and method shown, using a well-characterized resonator element 102 to provide an optical frequency reference signal does not necessarily require a modulator 110, since the spectral characteristics of the well-characterized resonator element that can be used can be determined by applying the methods of this disclosure. However, according to different embodiments, the apparatus for providing an optical frequency reference may also include a modulator to recalibrate the resonator element 102 when needed.

[0085] according to Figure 5 In the illustrated embodiment, resonator element 102 is used to provide an optical frequency reference signal for other applications. Further applications may include spectral characterization of photonic device 120 (e.g., miniature ring resonator 120). Due to the provision of an optical frequency reference and optional calibration element 118, the spectral characteristics (such as resonant frequencies) of photonic device 120 can be relatively, optionally, absolutely characterized by comparing the measured frequencies with the carrier resonance and / or sideband resonance of the provided resonator element 102.

[0086] Figure 6 A method for providing an optical frequency reference signal for a laser with a tunable carrier frequency is schematically described. This method can use a reference... Figure 5 The method is performed using the aforementioned apparatus. The method includes providing a resonator element 102 in step 602, the resonator element having a plurality of carrier resonances 3000 for a carrier frequency of the laser, wherein adjacent carrier resonances 3000 are spaced apart from each other in the spectral domain by their respective predetermined free spectral regions (FSRs). The method includes coupling a first portion of the laser to the resonator element 102 in step 604, and measuring the intensity of the laser portion transmitted and / or reflected by the resonator element 102 in step 606. Furthermore, the method includes providing, in step 608, a frequency of a tunable carrier frequency having local extrema in the measured intensity of the laser portion transmitted and / or reflected by the resonator element, this frequency serving as a spectral reference marker for an optical frequency reference signal defined by the predetermined free spectral regions (FSRs).

[0087] A detailed example will be provided below to demonstrate the proof of concept, but this embodiment or disclosure is not limited to this detailed example.

[0088] As a proof-of-concept demonstration, the characteristics of resonator element 102 were characterized by measuring its optical dispersion, thus validating the presented method and apparatus. Resonator element 102 is provided in the form of an optical fiber cavity. The optical fiber cavity is constructed from a 10 dB optical fiber coupler and a 5-meter length of standard telecommunications fiber (SMF-28), with a zero-dispersion wavelength of approximately 1.310 nm. The free spectral range (FSR) of the optical fiber cavity is approximately 39 MHz, and the mode linewidth is approximately 1 MHz, which limits the measurement speed to approximately 1 THz / s. See P. Del'Haye et al., “Frequency comb assisted diode laser spectroscopy for measurement of microcavity dispersion,” *Nature Photonics*, Vol. 3, pp. 529–533 (2009).

[0089] To demonstrate the ultra-high frequency resolution of the method and apparatus disclosed herein, a 1.3 μm tunable laser (tunable range 1.270 to 1.330 nm) was used as the laser source to resolve minute FSR variations near the zero-dispersion wavelength. In the experiment, the tunable laser was modulated at a first frequency of 1001f. mod1 Second modulation frequency 1002f mod2 Two 20GHz modulation signals with a frequency difference of 4MHz are provided for modulation. The two modulation signals are combined by a power combiner and applied to the EOM, which serves as modulator 110. The laser transmitted through the fiber cavity is detected by detector unit 112, which includes a photodiode (PD) and an oscilloscope, which serves as data logger 114, for recording measurement values. The oscilloscope has a memory depth of 31.25 million.

[0090] Figure 7 Section a) shows the transmission spectrum of the fiber cavity from 1.270 nm to 1.330 nm, with an inset showing magnified details near 1.300 nm. The vertical axis represents transmission in arbitrary units, and the horizontal axis represents wavelength in nanometers. The deeper dips in transmission are fiber cavity resonances generated by the tuned laser at the carrier frequency, referred to as carrier resonance 3000. The other four smaller dips within an FSR are formed by modulation sidebands and are therefore referred to as sideband resonances 3001 and 3002. Figure 7 Section b) shows the measured FSR of the fiber cavity as a function of wavelength near the zero dispersion region. Figure 7Section b) shows trace 7000 (left axis), illustrating the results calculated for the dual-RF modulation scheme. The left vertical axis represents the FSR minus the 38,906 MHz offset, and the horizontal axis represents the wavelength (in nanometers). Trace 7000 has a frequency resolution below 15 Hz, clearly resolving minute FSR variations (<800 Hz) within the 11 THz range and revealing the complex cavity dispersion of the fiber loop, from normal dispersion at short wavelengths to zero dispersion, and then to anomalous dispersion at long wavelengths. Trace 7002 is a second-order polynomial fit, with the zero-dispersion wavelength located at 1.315 nm. For comparison, Figure 7 In section b), trace 7004 (right axis) shows the evolution of the FSR calculated from measurements using only a single modulation frequency (20 GHz) as the modulating signal. The right vertical axis represents the FSR (trace 7004) minus an offset of 38,906 MHz. Figure 7 Section c) shows the frequency difference (trace 7006) between the FSR measurement plotted in trace 7000 and the fitted value plotted in trace 7002, where the vertical axis represents the difference in Hertz and the horizontal axis represents the wavelength in nanometers. Figure 7 Section d) shows histograms 7008 and 7010 based on the frequency difference of trace 7006 in section c), which demonstrates a root mean square deviation of 14.2 Hz. These results indicate that the disclosed dual-RF broadband modulation spectrometer has ultra-high frequency resolution.

[0091] according to Figure 7 The measurement results in part b) Figure 8 The upper part shows the calculated group velocity dispersion β2 of the fiber cavity along trace 8000, where the horizontal axis represents wavelength in nanometers and the vertical axis represents wavelength in ps. 2 The group velocity dispersion β² is expressed in units of / km. The results are in excellent agreement with the dispersion of standard telecommunications optical fibers. Figure 8 The trace 8002 in the lower panel shows the corresponding group delay dispersion (GDD) of the 5-meter fiber cavity, including dispersion from the 10 dB coupler. The vertical axis represents the dispersion in fs. 2 The group delay dispersion is expressed in units. By removing a 3-meter fiber from the cavity, the GDD of a 2-meter fiber cavity can be measured using a dual-RF modulation scheme (trace 8004 in the figure below), with a zero-dispersion wavelength of 1.318 nm. The GDD of a 3-meter fiber cavity can be obtained by subtracting the GDD of a 2-meter fiber cavity from the GDD of a 5-meter fiber cavity, as shown below. Figure 8The lower trace 8006 shows a zero-dispersion wavelength of 1.312 nm. Trace 8006 represents the difference between traces 8002 and 8004. The measurement results show that the longer the fiber length, the closer the zero-dispersion wavelength of the fiber cavity is to the zero-dispersion wavelength of the fiber itself. This demonstration proves that the disclosed method can be used to characterize the optical properties of individual devices, such as dispersion-engineered broadband mirrors and integrated photonic devices.

[0092] The above results demonstrate that for quasi-periodic structures with low FSR (FSR < modulation frequency), the dual-RF modulation scheme exhibits ultra-high frequency resolution according to the disclosed method. The application of the disclosed method will now be expanded to measure the mode spectra of devices with high FSR (FSR > modulation frequency), for example, based on... Figure 5 The optical micro-resonator of the device shown was used for measurement. In this measurement, an optical fiber cavity was used as the resonator element, and the carrier resonance of a 5-meter optical fiber cavity was provided as a frequency marker, i.e., as an optical frequency reference signal, to measure the resonant frequency of the separately fabricated Si3N4 resonator. The Si3N4 resonator was fabricated by depositing a 750 nm Si3N4 thin film and a 3 μm SiO2 layer on a silicon substrate using a low-temperature reactive sputtering method, see A. Frigg et al., “Low loss CMOS-compatible silicon nitride photonics utilizing reactive sputtered thin films,” Optics Express, Vol. 27, pp. 37795–37805 (2019).

[0093] Figure 9 The illustration in section a) shows a scanning electron microscope image of the Si3N4 microresonator used in the experiment, which has a diameter of 200 μm and a waveguide cross-section of 1.8 μm × 750 nm. The measured FSR and intrinsic optical quality are approximately 231 GHz and 2 million, respectively. Figure 5 As shown, a portion of the laser follows the same path as in the previous experiment, modulated using two selectable modulation frequencies, and is then injected into the fiber cavity. The transmitted signal is detected by photodiode 112 and recorded by one channel of oscilloscope 114. A portion of the laser is coupled into and out of a Si3N4 resonator through two lensed optical fibers; the transmission spectrum is recorded by another photodiode 112 and another channel of oscilloscope 114. Transmission signals from both the fiber cavity and the Si3N4 resonator are recorded simultaneously while scanning the frequency of the CW continuous laser. Figure 9Part (a) shows the normalized transmission spectrum of the Si3N4 resonator. Two distinct mode families were observed, with the star-shaped marker 9000 located in the mode family with the higher optical quality factor. The vertical axis represents transmission in arbitrary units, and the horizontal axis represents wavelength in nanometers. Figure 9 Part 4(b) shows a resonance near 1.271 nm in trace 9002 and the frequency marker 9004 of the fiber cavity. First, the FSR of the fiber cavity was calculated according to the dual-RF modulation scheme described above. Then, the calculated fiber cavity resonance was used as the frequency marker to measure the evolution of the Si3N4 resonator's mode structure, such as FSR, resonant linewidth, and dispersion. The vertical axis represents the amplitude in arbitrary units, and the horizontal axis represents the wavelength in nanometers.

[0094] The resonant frequencies of the mode family in a dispersive resonator can be described by Taylor series:

[0095]

[0096] Where μ is the number of patterns deviating from the central pattern (μ = 0), ω μ It is the resonant frequency. D1 / 2π is the FSR of the resonator element (i.e., the Si3N4 resonator) in the center mode (μ=0), and D2, D3, and D4 are the second, third, and fourth order dispersion coefficients, respectively. int It is integral dispersion, which represents the deviation of the resonant frequency relative to an equidistant grid with a spacing of D1. Figure 9 Section c) shows the measured integral dispersion curve (circled 9006) for the center mode at 1.310 nm, and the second-order polynomial fitting curve 9008 derived from the resonance marked 9000 in section a). The vertical axis represents D in gigahertz. int / 2π, where the horizontal axis represents wavelength in nanometers. The dispersion curve exhibits anomalous dispersion, with mode crossings at 1.280 and 1326 nm. To verify the dispersion measurements, a soliton frequency comb was generated at 1.310 nm using an optically pumped Si3N4 resonator. Section d) shows the fitted sech... 2 The optical spectrum 9010 of a single bright soliton in the envelope (dashed trace 9012) further confirms the anomalous dispersion mechanism of the pump mode. Furthermore, the mode crossover at 1.326 nm in section c) produces a dispersive wave at 1.326 nm in section d) (marked with arrows).

[0097] To further highlight the broad applicability and effectiveness of the disclosed method, its application in aperiodic structures was demonstrated, such as the analysis of absorption spectra in gas cells. This demonstration used an optical fiber-coupled hydrogen fluoride (H19F) gas cell at a pressure of 50 Torr and an optical path of 2.7 cm. Similarly, the laser from a 1.3 μm CW continuous laser source was split into two paths: one for probing high-frequency absorption spectra, and the other, modulated with dual RF signals, coupled to a 5-meter-long fiber optic ring cavity (as a resonator element), while simultaneously calibrating the laser frequency sweep.

[0098] Figure 10 Section a) shows the strong high-frequency molecular absorption lines (P and R branches) in the O-band range, where the vertical axis represents the transmittance in arbitrary units and the horizontal axis represents the wavelength in nanometers. Section b) shows the magnified spectrum (trace 10000) of the P(2) absorption line, with the carrier resonance 10002 of the fiber cavity as the frequency reference. Since the pressure broadening effect of the high-frequency gas is much greater than the Doppler broadening effect, the Lorentz function (dashed line 10004 in section b) is used to fit the spectral curve.

[0099] Table 1 shows the comparison between the measurement results of HF absorption lines and the HITRAN database (HITRAN database reference: IEGordon et al., “The HITRAN2016 molecular spectroscopic database”, Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 203, pp. 3-69 (2017)).

[0100] Table 1:

[0101]

[0102]

[0103] 1. Data from HITRAN is given after calibrating with a 50 Torr pressure offset.

[0104] The uncertainties in pressure offset and pressure widening linewidth are calculated based on a 20% pressure uncertainty.

[0105] 3. The measured R(2) is set to be equal to the value in HITRAN.

[0106] The second column of Table 1 shows the absorption line positions calculated from the HITRAN database, corrected for pressure offsets based on the vacuum transition wavelength. Columns 3 and 4 show the calculated Gaussian full width and Lorentz half-maximum full width (FWHM), respectively. Uncertainty was calculated based on a 20% uncertainty in gas pressure specified by the gas chamber manufacturer. Column 5 shows the measured spectral line positions. Since no absolute frequency reference is provided in this demonstration, the wavelength of the measured R(2) line is set to be equal to the value calculated from the HITRAN database. Column 6 shows the wavelength difference between the measurement results and the HITRAN database. As can be seen, the measurement results are in excellent agreement with the HITRAN database. This small difference can be attributed to the uncertainty in gas pressure. Using the Gaussian linewidth and Voigt function calculated in column 3, the last column shows the measured Lorentz full width for different absorption lines. Considering that the wavelength of the measured spectral line positions is smaller than the calculated value in column 2, and the measured Lorentz linewidth is larger than the calculated value, it is speculated that the pressure of the high-frequency gas chamber used as the calibration element in the experiment is higher than the manufacturer's specified 50 Torr.

[0107] In summary, this disclosure presents and demonstrates a powerful broadband spectroscopy technique based on a tunable CW laser, whose frequency scanning behavior is calibrated by a fiber cavity with dual RF frequency modulation capabilities. Using this method, minute FSR deviations (800 Hz) of the fiber cavity in a near-zero dispersion state can be resolved at a resolution of less than 15 Hz within an 11 THz frequency range. The demonstrated measurement speed is 1 THz / s, which is limited by the cavity linewidth of the fiber cavity, rather than by the measurement system of conventional devices (see P. Del'Haye's paper "Frequency comb assisted diode laser spectroscopy for measurement of microcavity dispersion", *Nature Photonics*, Vol. 3, pp. 529-533 (2009)). This speed can be significantly increased to over 10 THz / s if the resonator element has a wider linewidth (>3.2 MHz). Ultimately, the measurement speed is limited by the tuning speed of the laser source. Furthermore, the presented method surpasses the stringent requirements of traditional frequency comb-based spectrometers regarding spectral flatness, comb power, and polarization. The spectral range of the disclosed method is limited only by the tunable range of the CW laser, and can be extended by cascading multiple CW lasers (see J. Liu et al., “Frequency-comb-assisted broadband precision spectroscopy with cascaded diode lasers,” Optics Letters, Vol. 41, pp. 3134–3137 (2016)). It can also reach previously unattainable spectral regions where high-resolution wavelengthmeters or frequency combs are unavailable. We further validate the application of the disclosed method in characterizing the dispersion and high-frequency gas molecular absorption spectra of integrated photonic devices. Utilizing well-known atomic / molecular transitions as an absolute frequency reference, this method can be used for high-precision broadband molecular spectroscopy analysis (see A. Shkarin et al., “Nanoscopic Charge Fluctuations in a Gallium Phosphide Waveguide Measured by Single Molecules,” Physical Review Letters, Vol. 126, pp. 133–602 (2021)). Furthermore, the disclosed method can be widely applied to various scenarios, such as lidar (see E).Baumann et al.'s paper "Comb-calibrated frequency-modulated continuous-wave lidar for absolute distance measurements," Optics Letters, Vol. 38, pp. 2026-2028 (2013); three-dimensional imaging (refer to E. Baumann et al.'s paper "Comb-calibrated laser ranging for three-dimensional surface profiling with micrometer-level precision at a distance," Optics Express, Vol. 22, pp. 24914-24928 (2014)); refractive index measurement (refer to L. Yang et al.'s paper "Frequency combcalibrated frequency-sweeping interferometry for absolute group refractive index measurement of air," Applied Optics, Vol. 56, pp. 3109-3115 (2017)); precise frequency measurement and characteristic analysis of photonic devices (refer to V. Brasch et al.'s paper "Photonic chip–based optical frequency comb..."). “using soliton Cherenkov radiation,” *Science*, Vol. 351, pp. 357–360 (2016); “Precisefrequency measurement and characterization of a continuous scanning single-mode laser with an optical frequency comb,” *Opt. Lett.*, Vol. 39, pp. 4923–4926 (2014)); for example, astrophotonic devices (see “Astrophotonics: astronomy and modern optics,” *Astron. Astrophys. Rev.*, Vol. 29, p. 6 (2021)).

[0108] Figure 11 A LiDAR system 300 is schematically depicted, which includes means 200 for providing an optical frequency reference signal according to an optional embodiment. Figure 12 A gas sensing system 400 is schematically depicted, which includes means 200 for providing an optical frequency reference signal according to an optional embodiment.

[0109] List of reference numerals

[0110] 100 Devices for characterizing resonator elements

[0111] 102 Resonator Components

[0112] 104 laser source

[0113] 106 fiber optic cable

[0114] 108 Coupling Elements

[0115] 110 Modulators for modulation intensity and / or phase

[0116] 112 Detector Unit

[0117] 114 Data Logger

[0118] 116 Control Unit

[0119] 118 Calibration Element

[0120] 120 Photonic Device / Miniature Ring Resonator

[0121] 200 A device for providing an optical frequency reference signal

[0122] 202-214 Method and Steps

[0123] 300 LIDAR system

[0124] 400 Gas Sensing System

[0125] 602-608 Method Steps

[0126] 1001 First modulation frequency

[0127] 1002 Second modulation frequency

[0128] 3000 carrier resonance

[0129] 3001 Sideband resonance generated by the first modulation frequency

[0130] 3002 Sideband resonance generated by the second modulation frequency

[0131] 3003 The time interval between sideband resonances from two different modulation frequencies in the first scan

[0132] 3004 The time interval between sideband resonances from two different modulation frequencies in the second scan

[0133] 3005 Unknown time interval within adjacent carrier resonances

[0134] 7000 shows the traces of the results from the dual-RF modulation scheme.

[0135] 7002 shows the trace of the second-order polynomial fitting.

[0136] 7004 FSR Evolution of a Single RF Modulation Scheme

[0137] 7006 Frequency difference between the measured FSR and the fitted plot

[0138] 7008 and 7010 frequency difference histogram

[0139] Group velocity dispersion calculated by 8000

[0140] Group delay dispersion of different fiber lengths (8002, 8004, 8006)

[0141] 9000 is a family of modes with a high optical quality factor.

[0142] Resonance curve at 9002 1.271 nm

[0143] 9004 Frequency Marker

[0144] 9006 Integral Dispersion Curve

[0145] 9008 Fitted Curve

[0146] Optical spectrum of a single bright soliton (9010)

[0147] 9012 Fitted envelope curve

[0148] 10000 absorption line spectrum

[0149] 10002 carrier resonance

[0150] 10004 Fitted Lorentz function

[0151] FSR Free Spectral Region

Claims

1. A method for characterizing a resonator element (102), the method comprising: - Provides lasers with tunable carrier frequencies; - Couple at least a first portion of the laser to a resonator element (102) having multiple carrier resonances (3000) for a carrier frequency of the laser, wherein adjacent carrier resonances (3000) are spaced apart from each other in the spectral domain by a free spectral region (FSR). - The intensity and / or phase of said portion of the laser coupled to the resonator element (102) are modulated with a first modulation frequency (1001) and a second modulation frequency (1002), thereby generating at least two sideband resonances (3001) separated from the corresponding carrier resonance (3000) by the first modulation frequency (1001), and at least two sideband resonances (3002) separated from the corresponding carrier resonance (3000) by the second modulation frequency (1002), wherein the first modulation frequency (1001) and the second modulation frequency (1002) are not integer multiples of the free spectral region and are not the same as each other; - The carrier frequency of the laser is tuned at a predetermined tuning rate; - While tuning the carrier frequency, measure the intensity of laser transmitted and / or reflected by the resonator element (102); - Measure the tuning time of tuning the carrier frequency through four adjacent sideband resonances (3001, 3002), the tuning time being equivalent to the tuning time required to change the tunable carrier frequency from the value corresponding to the first resonance among the four sideband resonances to the value corresponding to the last resonance among the four sideband resonances. and - The interval between multiple carrier resonances (3000) in the spectral domain is determined based on the measured intensity of the laser transmitted and / or reflected by the resonator element (102) and the first modulation frequency (1001), the second modulation frequency (1002) and the measured tuning time of tuning the carrier frequency through four adjacent sideband resonances (3001, 3002).

2. The method according to claim 1, wherein the first modulation frequency (1001) and the second modulation frequency (1002) are both within the radio frequency range.

3. The method according to claim 1 or 2, wherein the first modulation frequency (1001) and the second modulation frequency (1002) are each in the range of about 100 MHz to about 100 GHz.

4. The method according to any one of the preceding claims, wherein the difference between the first modulation frequency (1001) and the second modulation frequency (1002) is not less than 10% of the resonant linewidth of the carrier resonance (3000) and not greater than 50% of the free spectral region (FSR).

5. The method according to any one of the preceding claims, wherein the first modulation frequency (1001) and the second modulation frequency (1002) substantially correspond to frequencies near multiples of n+1 / 2 of the free spectral region (FSR), where n is an integer.

6. The method according to any one of the preceding claims, wherein two sideband resonances (3001) generated by a first modulation frequency (1001) from one of the carrier resonances (3000) are located in at least one free spectral region (FSR), and at least two sideband resonances (3002) generated by a second modulation frequency (1002) from one of the carrier resonances (3000) are located.

7. The method according to any one of the preceding claims, wherein measuring the tuning time of the carrier frequency through four adjacent sideband resonances (3001, 3002) includes measuring the tuning time of the carrier frequency through four adjacent sideband resonances (3001, 3002) within a single free spectral region.

8. The method according to any one of the preceding claims, wherein the free spectral region (FSR) of the resonator element (102) is not less than 1 MHz and not greater than 100 GHz.

9. The method according to any one of the preceding claims further comprises: - Couple the second part of the laser to a calibration element (118) having predetermined absolute transmission and / or reflection characteristics; - While tuning the carrier frequency, measure the intensity of the portion of the laser transmitted and / or reflected by the calibration element (118); - Identify at least one specific absolute transmission and / or reflection characteristic of the calibration element (118), the absolute transmission and / or reflection characteristic having a predetermined frequency, the predetermined frequency coinciding with or having a specified offset from one of the carrier resonance (3000) or sideband resonances (3001, 3002) in the frequency domain; and - Based on the specific absolute transmission and / or reflection characteristics determined by the calibration element (118), calibrate the absolute frequency of at least one of the carrier resonance (3000) or sideband resonances (3001, 3002).

10. The method of claim 9, wherein the calibration element (118) comprises a gas chamber filled with a predetermined gas having at least one specific absolute transmission and / or reflection characteristic, and / or the calibration element (118) comprises one or more of the following elements: a frequency comb, a wavelength meter, or an element providing atomic and / or molecular transition lines.

11. An apparatus (100) for characterizing a resonator element (102), the apparatus (100) comprising: - A tunable laser source (104) for emitting laser light with a tunable carrier frequency; A coupling element (108) couples at least a portion of the laser beam to a resonator element (102); - A modulator (110) for modulating the intensity and / or phase of said portion of a laser coupled to a resonator element (102), thereby generating at least two sideband resonances (3001) at a first modulation frequency (1001) for each carrier resonance (3000) separated from the corresponding carrier resonance (3000) by the first modulation frequency (1001), and generating at least two sideband resonances (3002) at a second modulation frequency (1002) for each carrier resonance (3000) separated from the corresponding carrier resonance (3000) by the second modulation frequency (1002); - Detector unit (112), the detector unit (112) is used to measure the intensity of a portion of the laser transmitted and / or reflected by the resonator element (102); - A control unit (116) configured to determine a tuning time and an interval between multiple carrier resonances (3000) in the spectral domain based on the measured intensity of the laser transmitted and / or reflected by the resonator element (102) and based on a first modulation frequency (1001), a second modulation frequency (1002), and a measured tuning time for tuning the carrier frequency through four adjacent sideband resonances (3001, 3002), the tuning time being equivalent to the tuning time required to change the tunable carrier frequency from the value corresponding to the first of the four sideband resonances to the value corresponding to the last of the four sideband resonances.

12. The apparatus (100) of claim 11, wherein the resonator element (102) comprises an optical fiber cavity and / or an integrated waveguide resonator, and / or a whispering-gallery mode resonator and / or an Etalon resonator and / or a Fabry-Perot resonator.

13. The apparatus (100) according to claim 11 or 12, wherein the modulator (110) comprises an electro-optic intensity modulator and / or a phase modulator.

14. The apparatus (100) according to any one of claims 11 to 13 further includes a calibration element (118) having predetermined absolute transmission and / or reflection characteristics; The detector unit (112) is also adapted to measure the intensity of a portion of the laser transmitted and / or reflected by the calibration element (118) while tuning the carrier frequency; and The control unit (116) is further adapted to identify at least one specific absolute transmission and / or reflection characteristic of the calibration element (118), the absolute transmission and / or reflection characteristic having a predetermined frequency that coincides with or has a specified offset from one of the carrier resonance (3000) or sideband resonances (3001, 3002) in the frequency domain, and the control unit (116) is adapted to calibrate the absolute frequency of at least one of the carrier resonance (3000) or sideband resonances (3001, 3002) according to the identified specific absolute transmission and / or reflection characteristic of the calibration element (118).

15. The apparatus of claim 14, wherein the calibration element (118) comprises a chamber filled with a predetermined gas having at least one specific absolute transmission and / or reflection characteristic, and / or comprises a frequency comb and / or a wavelength meter and / or elements providing atomic and / or molecular transition lines.

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